This paper explores the effect of asymmetric conditions, specifically non-zero heel, on the formulation of the ship motion problem using a fully-coupled, linear seakeeping code developed by the author. A theoretical formulation is provided under the auspices of an eliminated symmetry assumption, and numerical predictions of the radiation and excitation forces are given to explore unique aspects of the problem. Symmetric and asymmetric numerical heave, roll, and pitch RAOs for a generic naval frigate are compared to third-party model test data. It is found that asymmetry can have marked effects on the ship motions problem, most notably in the roll excitation moment, physical mass matrix, and the hydrodynamic cross-coupling of the six modes of motion. The location of a so-called “center of motion” is found to be important in the formulation, suggesting that the origin cannot be arbitrarily placed at the center of mass. Some discussion addressing the practical nature of asymmetry in seakeeping computations is provided, attempting to relate the theoretical and numerical findings back to the practical application.
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